Question: Rewrite as a simplified fraction. ${2.\overline{27} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 227.2727...\\ 1x &= 2.2727...\end{align*}}$ Subtracting the two equations, we have: ${99x = 225}$ ${x = \dfrac{225}{99}} $ ${x = \dfrac{25}{11}} \text{or} {2 \dfrac{3}{11}}$